This is one of those very vague questions that is almost impossible to answer, certainly to solve. Is it possible? Well, anything is possible, as long as it does not involve the Cubs winning the World Series. Oh, wait. They won! ;-)
You need to define what you mean by "draping a curve". You might be thinking of something vaguely like a smoothing spline, or perhaps a least squares tension spline. Smoothing splines are pretty common, easy to find. Tension splines are a bit more rare, being somewhat nonlinear things. Smoothing splines are easier to work with and estimate, so are more common.
But if draping a curve means something completely different to you, well, it all depends on what you are thinking of.
